Generalization of Darbo-Type Fixed Point Theorem and Applications to Integral Equations

摘要

We propose a new notation of μ-set contractive mappings for two classes of functions involving a measure of noncompactness in Banach space and Darbo-type fixed point and n-tupled fixed point results. These results include and extend the results of Falset and Latrach [Falset, J. G., Latrach, K.: On Darbo-Sadovskii's fixed point theorems type for abstract measures of (weak) noncompactness, Bull. Belg. Math. Soc. Simon Stevin 22 (2015), 797-812.] The results are also correlated with the classical generalized Banach fixed point theorems. Finally, we apply these results to two different Volterra integral equations in Banach algebras with an illustration.